OEIS A212558: Proof of Unproven Conjecture? Proven!

12192017, 06:21 AM
Post: #9




RE: OEIS A212558: Proof of Unproven Conjecture? Proven!
Gerald, thanks you for the interesting quiz!
Small addendum about sum of the decimal digits of n. Let s(n) is the sum of the decimal digits of n. Consider condition 4*s(n)^2 < ns(n), (*) 4*s(n)^2 + s(n) < n Function in left is monotonically increasing function, then in respect that s(n) <= 9*log10(n+1) we get estimation 4*s(n)^2 + s(n) <= 4 * (9 * log10(n+1))^2 + 9*log10(n+1) = 324 * log10(n+1)^2 + 9*log10(n+1) Maximal solution of the equation 324 * log10(n+1)^2 + 9*log10(n+1) = n is n0 ~ 4313.68. (I use Wolfram Alpha for getting this value.) Hence, condition (*) is true for all n > n0. For n from 2999 to 4313 source statement may be checked by direct computations. 

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Messages In This Thread 
OEIS A212558: Proof of Unproven Conjecture? Proven!  Gerald H  12182017, 08:23 AM
RE: OEIS A212558: Proof of Unproven Conjecture?  pier4r  12182017, 08:26 AM
RE: OEIS A212558: Proof of Unproven Conjecture?  stored  12182017, 10:21 AM
RE: OEIS A212558: Proof of Unproven Conjecture?  Gerald H  12182017, 12:00 PM
RE: OEIS A212558: Proof of Unproven Conjecture?  Paul Dale  12182017, 10:27 AM
RE: OEIS A212558: Proof of Unproven Conjecture?  Gerald H  12182017, 01:29 PM
RE: OEIS A212558: Proof of Unproven Conjecture? Proven!  Paul Dale  12182017, 10:22 PM
RE: OEIS A212558: Proof of Unproven Conjecture? Proven!  Gerald H  12192017, 05:39 AM
RE: OEIS A212558: Proof of Unproven Conjecture? Proven!  stored  12192017 06:21 AM
RE: OEIS A212558: Proof of Unproven Conjecture? Proven!  Gerald H  12192017, 08:10 AM

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